2. a) Find the solution for the following differential equation: +47y = 0; y(0) = 1, y(0) = 0 b) Rewrite this equation in the state-space form (matrix form) and solve numerically by using bl) a first-order approximation to the derivative, i.e., i ~ y(t + h) y(t) b2) a second-order approximation to the derivative, i.e., ~ y(t + h) ylt h) 2h b3) using MATLAB's ode23 c) Plot the exact solution found in part (a) vs. solutions found in parts (b1) and (b2) for several h's as follows: h=0.1, 0.01, 0.001